Constraints not satisfied with 'ga' solver and integer variables

Hi all,

I've been struggling to understand what is the problem with my code. I wrote this long time ago, and now I'm using it with another dataset (large one) and is not working. I'm using 'ga' optimisation with integer variables, but I'm getting the legend of " Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance but constraints are not satisfied."

Basically what I want to do with my constraints is to avoid repetitions of the integer values in the vector of variables "x" (which has 42 values), and to make sure that the integer value selected for each "x" exists in the respective column of a matrix (124 rows, 42 columns). My LB and UB are between 1 to 124.

The results that I'm getting for the vector "v" are either very close to LB or UB, so 1 to 4 and 122 to 124. So I'm thinking that maybe is completely ignoring all the integer numbers and that's why it cannot find a solution. Here are the line where I call the ga:

x = [55 96 33 73 4 51 37 39 50 78 20 88 1 47 17 44 40 66 56 113 74 31 105 34 108 65 49 8 75 22 99 42 91 46 93 71 82 121 94 114 48 70];
LB=ones(1,42);
UB=zeros(1,42); UB(:)=124;
IntCon=[1:1:42];
hj=72;
options=optimset('Display', 'iter', 'FunValCheck', 'on');
[ x, fval, exitflag] = ga(@(x) ObjFun(x,TwoVal,distances, indices00,OrderedVal,hj,dimension00),42,[],[],[],[],LB,UB,@(x) constGa(x,OrderedVal),IntCon, options);

And the constraint function:

function [c,ceq] = constGa(x,OrderedVal)
ceq=[];
c1=length(unique(x)) == length(x);
c1=double(c1);
c1=(c1-1).^2;
ee=length(x);
for xe=1:ee
   c2(xe)= ~ismember(x(xe),OrderedVal(:,xe));
end
c2=double(c2);
c2=sum(c2);
c=[c1;c2];

If you have an idea what I might be doing wrong, I appreciate your suggestions. When I run this in a smaller dataset of 5 "x" variables instead of 42, and LB and UB between 1 to 18 instead of 1 to 124, I get a solution with satisfied constraints and minimum objective function.

Thank you, Martha

Answer 1

[Matt J]

It looks like a difficult feasible set, depending on what OrderedVal contains. It might help to formulate c,ceq in a form that is a bit less quantized,

function [c,ceq] = constGa(x,OrderedVal)

   c1=length(x)-length(unique(x));

   c2=min(abs(bsxfun(@minus, Ordererval,x(:).')));

ceq=[c1,c2];
c=[];

[Martha]

Thank you for your response Matt,

Yes, my only feasible points depends directly on what OrderedVal contains. I tried with the constraints formulated as you suggested, and I get "x" values results that are within a broader range, but still no solution found, and with many variables repeated.

[Matt J]

Perhaps there is no feasible solution. We would have to see OrderedVal to analyze that better.

[Martha]

Hi Matt, and thank you for your answer.

OrderedVal is very large to post here, but maybe is easy to explain. In the dataset that I'm using now 'OrderedVal' is a 124 x 42 matrix, the number of row and columns values can change, but there is always more rows than columns. For each column there are integer values from 1 to 124 randomly located. However, not all the rows have values, for each column the max, number of integer is 124, but for example some of the columns only have 20 values and from 21:124 there are NaNs. This is a very small example, where OrderedVal is a matrix of 18 x 5:

OrderedVal =
   16     1    16    15     1
  14    15    12    16    18
  15    17     2    12    16
  12    16     1    18    12
  18    18    15    17    15
   2    12     9     2     2
   9     2    18     1     9
  17     9    17     9    11
  11    11    14    14    17
  13    14    10     5    14
   5    13    11    10    13
   6     5     5    11     5
 NaN     6    13    13     6
 NaN   NaN     7     7   NaN
 NaN   NaN     8     8   NaN
 NaN   NaN   NaN   NaN   NaN
 NaN   NaN   NaN   NaN   NaN
 NaN   NaN   NaN   NaN   NaN

In this case, my problem seeks to find the best possible combination of 5 integer values without repetitions, that will result in the smallest value of the objective function. For examples with small dataset like this of 18x5 matrix the ga solver works fine. But when I'm trying to use it for bigger datasets it doesn't.

Let me know if you can think about what I'm doing wrong. Thanks,

Martha

[Matt J]

OrderedVal is very large to post here

You can attach .mat files. In any case, the feasible region consists of highly non-contiguous pieces. This makes it very difficult for the solver to find and optimize over. Are you sure it's non-repetitions in x(i) that you need, rather than OrderedVal(x(i),i)?

[Martha]

Hi Matt,

Yes, I'm sure about the non repetitions of 'x', so at the end I need to end up with 1 row for each column of my 124 x 42 matrix, with an integer number in each element that is unique, and that would be my x.

[Matt J]

I think we need to see the full problem description, including the objective function.

[Martha]

Hi Matt, Here is the objective function:

function a = ObjFunA(x,TwoParts,dim, OrgVal,OrderedVal,dimTotal)
klp=size(dim); klp=klp(1);
differences=zeros(1,klp);
for lp=1:klp
  Part1=TwoParts(1,lp); Part2=TwoParts(2,lp);
  Val_1=x(Part1); Val_2=x(Part2);
  n=dim(lp);
  Temp1=find(OrgVal(:,Part1)==lp);
  Temp2=find(OrgVal(:,Part2)==lp);
  id1=find(OrderedVal(:,Part1) == Val_1);
  id2=find(OrderedVal(:,Part2) == Val_2);
  q1=dimTotal(id1,Part1,Temp1);
  q2=dimTotal(id2,Part2,Temp2);
  additions=18;
  Total=((q1+q2)/2)+additions;
  Space(lp)=n-((q1+q2)/2);
  sumDim(lp)=(Space(lp)-additions).^2;
end
a=sum(sumDim);

I hope is not confusing, the value of "x" indicates to select an specific element for many combinations of elements that I have. In this case "klp" is the number of total combinations that I need to analyse. I need to find the best combination of "x" values that give me the minimum value of "a". However, I know that most likely "a" will never be zero. I just need to find the best combination with the minimum value of "x".

Thank you, Martha